The revolutions of computing and communication have opened up demands for the high quality of service (QoS), such as high data transmission, high reliability, and low latency. These new opportunities have spawned numerous studies on edge computing and artificial intelligence (AI), even the cooperation between them, referred to as edge intelligence. However, there are a number of handicaps that prevent edge intelligence from being used as a generic platform. The most intractable one is the heterogeneity and un-credibility among edges, hindering the way of sharing the learning results reliably, flexibly, and efficiently. In this paper, we propose a blockchain-assisted edge intelligence (B-EI) approach to solve the problem. The edge learning nodes train their local intelligence, followed by the improved blockchain to share the local intelligence, constructing edge intelligence among the heterogeneous and uncredible edges. Specifically, the improved blockchain employs a novel learning-measured consensus protocol, named Proof of Learning. The edges, also acted as the blockchain nodes, compete to have more superior local intelligence, instead of solving a hashed result. The superior local intelligence is then shared and distributed with other edges. It is not only beneficial to achieve edge intelligence, but also efficient to employ the computation resource, by replacing the hashing as the intelligence training. In order to show the potential benefits, we then use the proposed B-EI approach to solve a joint resource assignment problem. Simulation results show that our scheme outperforms the other state-of-art solutions, in terms of training episodes, and resource utility.